Windows Phone 8.1 games not showing in xbox live account

Hi,
I've got a Nokia Lumia 925 with Windows 8.1 and the latest updates installed. I also have an Outlook.com email account registered with the phone. The phone is also shown as a device on my Microsoft account.

I have an Xbox live account using the same outlook.com email address. I have the free version of Xbox live.

My Gamertag is exactly the same on my Windows Phone and my Xbox account. So no issues there.

I've recently started to play games on my Windows Phone and so far have two games installed. They are: -
Lara Croft Relic Run
Dredd vs. Zombies
The games play absolutely fine and they show up in the Games App on the phone.

The problem is they do not appear on my Xbox live account, when I log into my Xbox account on the web. I was expecting the games to show in the My Games tab. Apart from my avatar and Gamertag nothing else is on my Xbox account.

Why do the games not show on the Xbox live account?
Is it because I've only got the free version of Xbox live?
Or is it because Windows Phone 8.1 doesn't sync with Xbox live accounts.
Is it because I don't own an Xbox console?